I have never before posted on a thread like this, as it is too close to home and I'm always aware that my feelings and views might not be totally rational or reasonable, but your situation touches me so much.
6 years ago, I was you. My husband of 18 years dropped the same bombshell (it was a Saturday morning) and then went off for the day 'to think', leaving me at home with our 3 children, reeling from the enormity of what he'd just told me, whilst trying to act 'normal' for the children.
I know this may well not be the case in your situation, but it much later transpired that my husband that day went to do his 'thinking' with the OW, planning their future.
All the same thoughts you are thinking went through my head on a loop - how on earth was I going to manage without him, physically, financially, emotionally, but a part of me was very clear that if he wanted out I wasn't going to beg and plead him to stay - if he stayed it had to be because he wanted to, not because he felt obliged or guilty.
Sorry, I have no advice for you, because my marriage ultimately did end, but I just wanted you to know I totally understand how you feel at this time. I hope this is a blip for you, nothing more, but if it is more, you will cope and you will be fine.
Apologies if all this sounded tactless and blundering.